This page is for analysis of season four episodes NUMB3RS, for which the We All Use Math Every Day (WAUMED) activity program changed from providing PDF worksheets to providing a weekly blog with some new activities and links to past activities. A blog entry now appears approximately one week after the corresponding episode airs; despite this, the entries contain many errors in quoting characters from the episodes.

The web site of NCTM (National Council of Teachers of Mathematics) no longer promotes the television program or the activity program.

"None of the feedback indicated teachers were using the activities prior to the show airing on Friday nights. We talked to people who came to the WAUMED booth at the NCTM regionals and national conference…to those who stood line for autographs when [actor] Dylan [Bruno] was at NCSM [National Council of Supervisors of Mathematics] and surveyed the thousands who received the weekly emails (36 responded)." WEAUMED blogger tomlinson

Legend for blog comments below:

U = activity is
useless as a tie-in to the episode, referring to events or dialogue that do not
appear in the episode

E = activity
contains errors in mathematics or describing events or dialogue from the episode

NC = activity is
based on math that is not related to solving crimes

9/28/07 "Trust Metric"

10/5/07 "Hollywood Homicide"

10/12/07 "Velocity"

10/19/07 "Thirteen"

10/26/07 "Robin Hood"

11/2/07 "In Security"

11/9/07 "Primacy"

11/16/07 "Tabu"

11/23/07 "Graphic"

12/14/07 "Chinese Box"

1/11/08 "Breaking Point"

**9/28/07 "Trust Metric"**

Ironically, in this episode Charlie's main supposed mathematical contribution, his trust metric, is useless. When Charlie explains his results, Don asks, "What does that tell us?" and Charlie responds, "Nothing." Also, Charlie supposedly uses "set covering deployment" to try to find Colby. Though Don and his agents find Colby and Carter using Charlie's work, they escape, and thus Charlie's work was not ultimately useful.

The "Nash Equilibria" portion of the weekly episode blog begins, "In this episode, Charlie teaches a small Introduction to Game Theory class." In the episode the name of Charlie's course is not mentioned.

**10/5/07 "Hollywood Homicide"**

In a gross display of unethical, unprofessional behavior, Charlie submitted one paper to "a couple of journals to see if there was any interest in publishing it."

[NC] The weekly episode blog contains five segments, two of which are not related to math used to solve a crime. The "Beauty in Mathematics" section is related to a short conversation between Charlie and Larry on what Larry calls "transcendency" and looking for humanity in mathematics. The "Random Apollonian Networks" section begins, "Charlie mentions this topic as part of his research." In fact Larry is the one who mentions this topic, and it is merely a math buzzword with no hint of explanation.

Charlie's original contribution is to surmise that the car that crashed into the cafe had to have been approximately 260 pounds heavier than was reported. A look at a video recording shows that a 140-lb man had been in the trunk. Charlie's next guess is that the extra weight was from "briefest contact between the two vehicles." A video model of a Pitt maneuver is shown to a suspect who confesses.

Charlie looks at a grid of numbers on a wall at a crime scene and says "Fibonacci sequence," with no explanation of what that is, and without any of the numbers shown appearing to belong to the Fibonacci sequence. He is shown a grid of numbers found at a previous crime scene, and he circles strings of digits on that grid, but they are not Fibonacci numbers. This work leads Charlie to write down a new 7-digit sequence, 5550164, supposedly bridging the two grids, which turns out to be the cell phone number of the next victim of the serial killer. Thus "Fibonacci sequence" turned out to be just a buzzword.

In some very good luck, Amita reads Bible version Isaiah 53 and then enters the number 153 into some unexplained computer decryption program and it returns a street address where another beheaded victim and number sequence are found.

The "Fibonacci sequence" portion of the weekly episode blog contains a major misuse of terminology when it says, "The Fibonacci sequence is a series of numbers...." The following sentence ends with a question mark as opposed to a Greek letter: "These ratios approach the number 1.61803399…, which is known as the “golden ratio,” often represented by the Greek letter Phi (?)."

The "Enumerative combinatorics" portion of the blog makes quite a sweeping historical generalization when it says, "Eratosthenes was yet *another* Greek mathematician. (It seems like everyone was a Greek mathematician back then!)"

In this episode, Charlie supposedly uses "machine learning and recommender systems" to determine that the nine charities, all local and serving youth, all served the public through a common location, Promises House, a teen center that had been destroyed by a fire. This would have been found by a routine investigation. The case moves forward because Megan has Colby and David follow the shifty bank owner, who leads them to a money drop that then leads to a recovered license plate belonging to the career arsonist. The plate's owner immediately confesses and tells the whole story of how the bank owner had hired him to torch the teen center.

[E] The "Hand-path Analysis" portion of the
weekly episode blog contains errors in Charlie's quote: "Charlie says, 'By
watching and analyzing the swing, ~~you~~ *we* can tell from
the point of impact ~~exactly~~ where *exactly* the ~~
golf~~ ball ~~will~~ *is gonna* end up without ever
looking at the fairway." The blog continues, "It ball [sic] follows a
parabolic path."

It appears that the quote in the "Robin Hood Math" portion of the blog by Ann Valera, with no citation other than a hyperlink, was taken from an unrelated February 2007 publication.

[NC] The "405 is divisible by 9" portion of the blog is not related to the episode or the solving of crimes. The author is just thinking about numbers: "That led me to observe that the number 405 is evenly divisible by 9...." The title of this portion of the blog is in quotation marks for some reason.

[E] The "Fields Medal" portion of the blog
contains errors. "Charlie asks Amita, 'Do your [sic] really think I'll win
~~the~~ *a* Fields?' Amita replies, 'I do. Why
else do you think ~~I go~~ *I'm* with you.'"

At the 46-minute mark, Charlie's first contribution is non-mathematical, snooping in a computer database and finding out that Frederickson had accessed Don's file days before Leah's murder. Later he somehow decodes a message in graffiti.

Charlie and Amita make out in his office with the door open during the school day. Charlie whines about an upcoming "ridiculous TV interview" to promote his book "The Attraction Equation" which is in Amazon's Top 100 before any publicity. He is disheveled with unkempt hair, tie askew and an unironed shirt during his interview, when he says, "I developed a new kind of math...."

The opening numbers include "40 million" instead of "40,000,000."

Charlie makes no helpful math contribution for the agents. At the 48-minute mark, Amita builds something to decode some mpeg video to find out where the satellite phone source that sent it is located.

[E] The "Cake Cutting" portion of the blog
contains errors in Charlie's quote: "In the episode, the FBI negotiator
mentions that he had read some of Charlie's work on cake cutting, to which
Charlie responded, 'Sometimes cake is a series of algorithms *that help
formulate an analysis* and ~~sometimes it~~ *other times cake*
is just cake.'"

[E] The "Tabu Search Optimization" portion of the blog contains three large tree diagrams arranged vertically, but at one point the text says, "The shortest route following Dijkstra's algorithm results in the tree to the right." The word "tabu" is alternately capitalized and not capitalized.

[E, NC] The "Game Theory" portion of the weekly
episode blog contains errors in Charlie's quote: "Charlie says to his
class '~~People wonder~~ how game theory can be applied to casual
relationships. ~~With~~ *Between* friends, what's the
strategic goal? *After all,* There's no commodity being sought,
right? *Let's think about this.* ~~But, actually~~
even the most ~~causal~~ *casual* relationship is built around
a very important commodity: information. When a friend shares
information, they place a value on our intention not to use it against them.
And we* in turn* are expected to share our information with them."

[E] The "Fractal Number" portion of the blog
contains errors in the following quotes. "As Charlie says, 'Fractal Number
Estimate. It's based on Mandelbrot's use of fractal dimension to measure
the jaggedness of a coastline.' I~~t's been used to detect forged
handwriting, but we're applying it because hand-drawn art can be evaluated with
the same process.~~ **Amita:** ~~We use~~ *
'I am using* the fractal dimension analysis to evaluate the wrinkliness of
~~the~~ *these* lines.' **Charlie: ** 'An
authentic piece of handwriting or drawing will have a smoother ink edge, ~~
then~~ *than* one that is forged. *So, for instance, when I
sign my own name, the pen moves quite rapidly. The* Movements of the
hand are fast and fluid, *thus* minimizing contact between paper and pen.
The faster the hand movement, the smoother the ~~edges~~ *edge*
of the ink. *However*, When someone copies ~~the~~ my
signature, ~~they imitate the movements~~ *it's an imitation of
my movement*. It's not natural for the forger, ~~thus~~ so
it's slower. The slower the pen, the longer the contact with the paper,
~~allowing~~ *and* more ink to be absorbed. ~~
Creating~~ *which creates* a more irregular or wrinkly edge.
Fractal Dimension allows us to compare the wrinkliness and detect ~~which
is~~ the fake.' "

[E] The "Jump Bedding and Auction Theory"
portion of the blog entry contains no activity. Again there are many
errors in the transcription of Charlie's quotes: "As Charlie says, 'In
Auction Theory we talk about equilibria or symmetry. All *the*
bidders ~~should~~ have the same exact information. ~~
But in this case,~~ *Except* ~~the criminal~~ *Seth*
knows something the other bidders don't know *which is that the original copy
of Ultraworld #1 will be an item up for bid.* ~~This is~~
*So* asymmetrical information. ~~And this can create~~
*creates* asymmetrical bidding. This asymmetry will almost certainly
~~lead to something~~ *create a situation* called jump
bidding. ~~That's~~ *which is* when a person enters a
~~bid~~ far larger *bid* than ~~what's~~
necessary to be the current winning bidder. ~~Think of it~~
It's like a bike race. Typically, there's no advantage to jumping ~~
out~~ ahead of the pack. *So* The racers tend to stay
clustered together and switch off the leads. But there is a strategy of
taking the lead early to exhaust the competition. Jump bidding is like
quickening the speed of the race. It encourages the early exit of *some*
bidders, *and* discourages *the* late entry of others.' **
Megan:** 'So ~~during the auction~~, when someone makes a
big bid *during the auction*,' ~~that person should be the criminal~~.
**Charlie**: '*That's Seth's straw man*.' "

This portion of the blog entry states, "At the end of the episode, Charlie's father tells a magazine writer, 'Charlie thinks mathematics is beautiful and he wants everyone to love it the way he does." In fact this takes place at the 47-minute mark, and Charlie's father says "math" instead of "mathematics."

[E, NC] The blog entry contains errors in
Charlie's and Alan's quotes: "Alan comments, 'You ever notice ~~how~~
the first ~~elevator~~ *car you get* is always going the wrong
way?' Of course, Charlie cannot resist the opportunity to talk math with
his father. 'Actually, the Elevator Paradox accounts for that ... any one
elevator spends most of its time in the larger section of the building, ~~
and is~~ *so that's* more *than* likely ~~to come from
that direction~~ *the direction it's coming from* when you hit the
call button. If ~~you stood~~ *we were to stand* here
for several hours....'"

The blog states, "The Elevator Paradox was first noted by George Gamow and Moritz Stern, two physicists with offices located on the second and sixths [sic] floors, respectively, of a seven-story building." The correct name is Marvin Stern.

The blog author writes, "As a former electrical engineer for the Otis Elevator [sic], I can't help but be amused at the irony of writing this particular blog." This is an example of coincidence, not irony.

[E, NC] The blog entry contains errors in
Charlie's quote: "Colby says they know the motive is revenge, and Charlie
replies, '*That'*s true. But each ~~one~~ *suspect*
~~has been~~ *is* motivated to a different degree.
~~Think of~~ *You know* that ~~cool~~ carnival
game where you shoot a squirt gun ~~in the~~ *into a* clown's
mouth ~~in order~~ to fill ~~your~~ *up a*
balloon. An Asymmetric Threat Assessment allows us to measure the factors
that feed motive in each suspect ~~in the same way~~ *just like*
the mechanism of the game measures the flow of water into each clown's mouth.
It doesn't matter ~~whether~~ *if* the suspects *all*
have the same motive ~~or not~~. We ~~only need~~
*just have* to ~~identify~~ *find* the one case in which
~~the~~ motive has been fed to the point where the suspect
eventually pops'."

[NC] One of the four sections of the blog entry is on factorials, since Charlie's board has the number 28! written on it as part of his threat assessment, which he admits revealed "nothing unusual. No one stands out." Charlie's contribution to solving the case came at the 50-minute mark, when he determines that the strings of numbers found in the missing reporter's notes represent property ID numbers, square footage and assessed values of properties, though the data had somehow been "obscured." Thus he simply broke a code.

[U, E] The blog entry states, "One method to analyze large amounts of data is to use Checksum calculations (a pre-production version of the script for this episode indicates this as Charlie's approach, but that detail may have been lost in production.)" In fact there is no mention of such calculations in this episode. A user comment from January 16 identifies an error in an example in the blog entry. A reply from February 13 states that the error has been corrected.

** Note**: Even though 7 more episodes have aired this season,
and the blog entries are supposed to appear after the episodes air, the WAUMED
page now says, "Due to delays in new episodes and the writer’s strike we will
not be posting new blogs for the remainder of the 2007/08 school year. Thank you
for your support and we wish you the best on your end-of-year tests."

Episodes in the first three seasons are analyzed on a separate page.

This page was created and is maintained by Dr. Andrew Nestler at Santa Monica College.